Ch. 3 Flashcard

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis. It is also known as the initial value in a linear function.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the relationship between the slope and the steepness of a line?

Back

A greater slope value indicates a steeper line, while a smaller slope value indicates a less steep line.

Front

What is the initial value in a linear function?

Back

The initial value is the value of y when x is 0, which is the same as the y-intercept.

Front

What does it mean if a function has a positive slope?

Back

A positive slope means that as x increases, y also increases, indicating a direct relationship.

Front

What does it mean if a function has a negative slope?

Back

A negative slope means that as x increases, y decreases, indicating an inverse relationship.

Front

What is the formula for a linear equation?

Back

The formula for a linear equation is y = mx + b, where m is the slope and b is the y-intercept.